Exponentiated models preserve stochastic orderings of parallel and series systems |
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Authors: | Narayanaswamy Balakrishnan Abedin Haidari |
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Institution: | 1. Department of Mathematics and Statistics, McMaster University, Hamilton, Canada;2. Department of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran, Iran |
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Abstract: | AbstractIn this paper, we establish that the usual stochastic, hazard rate, reversed hazard rate, likelihood ratio, dispersive and star orders are all preserved for parallel systems under exponentiated models for lifetimes of components. We then use the multiple-outlier exponentiated gamma models to illustrate this result. Finally, we consider the dual family with exponentiated survival function and establish similar results for series systems. The results established here extend some well-known results for series and parallel systems arising from different exponentiated distributions such as generalized exponential and exponentiated Weibull, established previously in the literature. |
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Keywords: | Parallel system series system multiple-outlier exponentiated gamma model stochastic orders weak majorization order exponentiated models |
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